Allometric scaling enhances stability in complex food webs

Abstract

Classic local stability theory predicts that complex ecological networks are unstable and are unlikely to persist despite empiricists' abundant documentation of such complexity in nature. This contradiction has puzzled biologists for decades. While some have explored how stability may be achieved in small modules of a few interacting species, rigorous demonstrations of how large complex and ecologically realistic networks dynamically persist remain scarce and inadequately understood. Here, we help fill this void by combining structural models of complex food webs with nonlinear bioenergetic models of population dynamics parameterized by biological rates that are allometrically scaled to populations' average body masses. Increasing predator-prey body mass ratios increase population persistence up to a saturation level that is reached by invertebrate and ectotherm vertebrate predators when being 10 or 100 times larger than their prey respectively. These values are corroborated by empirical predator-prey body mass ratios from a global data base. Moreover, negative effects of diversity (i.e. species richness) on stability (i.e. population persistence) become neutral or positive relationships at these empirical ratios. These results demonstrate that the predator-prey body mass ratios found in nature may be key to enabling persistence of populations in complex food webs and stabilizing the diversity of natural ecosystems.

Positive complexity–stability relations in food web models without foraging adaptation

“…In the cases where we found negative complexity-stability relations in spite of decreasing mean interaction strength as, for example, in the niche model, additional mechanisms like unfavorable topological characteristics have to be invoked to explain the low robustness. We also investigated the effect of allometric scaling (Brose et al, 2006;Yodzis and Innes, 1992) on the network robustness. In agreement with (Brose et al, 2006;Yodzis and Innes, 1992), we found that the inclusion of body-size effects generally increases robustness, however we did not find that it can invert the sign of the complexity-stability relation.…”

“…We also investigated the effect of allometric scaling (Brose et al, 2006;Yodzis and Innes, 1992) on the network robustness. In agreement with (Brose et al, 2006;Yodzis and Innes, 1992), we found that the inclusion of body-size effects generally increases robustness, however we did not find that it can invert the sign of the complexity-stability relation. In the present study, we analyzed the population dynamics in food webs with constant interaction strengths.…”

“…When investigating the niche model, some authors use a modification where the number of basal species (species that feed from the resource) is kept constant (Kondoh, 2005;Brose et al, 2006). This is done because otherwise the number of basal species decreases with increasing C. In this way, Kondoh (2005) could obtain positive complexity-stability relations when including foraging dynamics into the model.…”

Food webs: reconciling the structure and function of biodiversity

“…This means that it is possible to model how factors such as the functional responses in consumer-resource interactions [33], adaptive consumer behaviour [34], and body-size distributions across species [35] influence biodiversity in complex communities. For example, in multi-trophic level food webs where coexistence of primary producers is strongly limited by competition for abiotic resources, dynamic models demonstrated that top-down control is necessary to prevent competitive exclusion and thus species loss [35]. These dynamic models predict species interactions by the body sizes of the taxa using empirically well-supported allometric scaling relationships of functional attributes such as metabolic and feeding rates with body sizes.…”

“…Although food webs ideally integrate ecological levels from individuals to populations to ecosystems, most work has occurred at the population level. Much recent effort has focused on extending predator-prey population dynamics to food webs, and has shown emergent food-web attributes, which result from interactions of population-level dynamics [34,35]. Even more complete models that include individual variability in consumption and competition and incorporate evolutionary dynamics have now been developed [40].…”